The simple harmonic oscillator is every instructor's favorite 216 problem to help with in the Math Lab. We'll solve this classical problem in the Hamiltonian formulation of mechanics before moving on to the quantum analogue. This is one of the most important problems in quantum mechanics and one of the few which has exact analytic solutions. After studying the solutions in the most common representation of the relevant operators, we'll discuss the uniqueness of this representation and the Stone-von Neumann theorem. Speaker(s): Joe Kraisler (University of Michigan)